This invention relates to an efficient energy storage flywheel possessing a benign failure mode. The invention relates particularly to flywheels with rotors fabricated from single crystals, microcrystalline solids, glasses or glass ceramics, which materials possess both high strength and low density and which fail at high stress in a brittle manner, thereby assuring rapid and complete fragmentation of the rotor in the event of rotor burst.
Flywheel based energy storage devices have long been regarded as having considerable promise for a variety of automotive, spacecraft, utility power and other applications due to their intrinsic simplicity, non-polluting nature, high efficiency and long cycle life compared to chemical batteries and other conventional energy storage means. A flywheel stores energy as the kinetic energy of a rapidly rotating body. The stored kinetic energy is proportional to the square of the rotation rate which is limited by the strength of the centrifugally stressed rotor. As a consequence, the energy stored per unit weight, or the specific energy of a flywheel, is directly proportional to the specific strength of the rotor material .sigma./.rho., where .sigma. is the breaking strength and .rho. is the density of the material. Hence, high strength, low density materials are preferred for flywheel rotor construction.
A wide variety of geometrical and mechanical designs have been proposed for energy storage flywheel rotors but most of these can be conveniently grouped into two categories based on the directionality, or lack thereof, of the rotor material mechanical properties. Isotropic materials possess nearly equal strengths in all mechanical properties. Isotropic materials possess nearly equal strengths in all directions whereas anisotropic materials, such as fiber reinforced composites, have strong directionality of mechanical properties. In the present invention, the term "isotropic" shall refer to materials in which the variation of strength with direction in the plane of rotation is less than 25%.
The simplest rotor designs employ materials with substantially isotropic mechanical properties, typically metallic alloys such as steel, titanium or aluminum, fabricated into disc-like shapes. The optimal designs for disc-like isotropic flywheel rotors are based on the so called Stodola or "optimized" shapes in which the thickness of the rotating disc decreases hyperbolically or exponentially with increasing radius in such a way that the magnitude of the centrifugally generated stress is only weakly position dependent or constant throughout the rotor body. The mathematical basis of constant stress rotor designs is described by Kulkarni and Stone in U.S. Pat. No. 4,408,500 and by J. P. Den Hartog in the book Advanced Strength of Materials, McGraw-Hill, 1952, pp. 49-69, all incorporated herein by reference. Since the ideal Stodola shape extends to infinity in the radial direction and is thus not suited for practical use, Kulkarni and Stone teach a modification to the Stodola design in which the rotating disc is truncated at a finite radius and the thin edges are thickened to increase the total kinetic energy relative to a truncated but not edge thickened Stodola design. The maximum energy storage per unit mass of a Stodola flywheel is numerically equal to .sigma./.rho..
Unfortunately, the performance and safety of isotropic rotors are limited by the mechanical properties and fracture behaviors, respectively, of conventionally chosen rotor materials. For example, the highest performance steels may have tensile strength values .sigma. approaching 300,000 lb/in.sup.2 and density .rho. is near 0.283 lb/in.sup.3. The cyclic fatigue behavior of high strength steels limits design stresses to about 90,000 lb/in.sup.2, giving an available specific strength for energy storage applications of about 318,000 inches, equivalent to 856,000 ftlb/slug maximum specific energy. Marginally higher specific strength can be obtained using certain titanium alloys but the improved properties come at significantly higher cost compared to steel.
Metal alloys for structural applications are generally processed to possess significant ductility so that tensile crack propagation is impeded and stabilized, giving rise to predictable fracture characteristics. However, these otherwise favorable mechanical behaviors of ductile metallic alloys give rise to problems in high speed rotor applications. Catastrophic rotor burst failures have been associated with the use of ductile isotropic metal alloy rotors at high rotational speeds. In a typical failure of this nature, the ductile rotor fractures into several relatively large ballistic particles which, as a group, carry the entire stored energy of the rotor, and are individually capable of inflicting very severe damage and/or injury in the surrounding area. This potential for ballistic damage and injury has heretofore limited the practical applications of isotropic rotors to relatively low energy applications such as in momentum control wheels for spacecraft.
Anisotropic flywheel rotor designs typically start with a rotating tensile ring or tube made from carefully wound fiber-reinforced uniaxial composite. This design concentrates mass at the largest radius and directs fiber strength in the tangential or hoop stress direction. Carbon fibers are often chosen because of their high specific strengths. Carbon fibers with strengths as high as 750,000 lb/in.sup.2 and density near 0.065 lb/in..sup.3 are available commercially. Carbon fibers typically have round cross-sections and, with careful winding, packing density in the wound fiber composites up to 78% can be achieved. The remaining space in the composite is filled with matrix resin. The composite matrix resin contributes weight but not strength to the rim thereby diluting the properties of the high strength fiber. This factor limits the strength of the resulting carbon fiber composite to about 585,000 lb/in.sup.2. Assuming that the resin density is approximately equal to that of the carbon fibers, the specific strength of the carbon fiber composite rotor is still approximately 9.000,000 inches equivalent to 24,000,000 ftlb/slug or more than an order of magnitude better than that of high strength steels.
However, difficulties in the design of composite rotors are introduced by the extremely low transverse strength of uniaxial composites. This weakness can lead to delamination under the significant radial stresses experienced by the rotor if it has significant thickness in the radial direction. Thus, while the energy storage efficiency of a rotating anisotropic rim can be large on a per unit weight basis, it difficult to achieve high volumetric efficiencies. Moreover, high levels of energy storage imply high elastic strain values in rotating rim flywheel designs. Centrifugal stress and strain values in the hub and axle sections of the rotor are much lower due to the smaller radius of rotation. Means for mechanical coupling the rim to the hub and axle sections of the rotor must be sufficiently compliant to accommodate this large radial differential in elastic strain while, at the same time, sufficiently stiff to resist input/output torques and gyroscopic twisting forces and to maintain stability with respect to potentially destructive vibratory modes. Many complex mechanical constructions have been advanced to meet these requirements. For example, Friedericy et. al., in U.S. Pat. No. 4,036,080, show a flywheel rotor with multiple nested composite rims which frictionally couple inertial torques to a hub while largely decoupling radial stresses. Additionally, Bakholdin et. al., in U.S. Pat. No. 5,628,232, teach the use of conical sections combined with cylindrical hubs to mechanically couple a rotating annular cylinder to a rotating shaft while Bitterly, in U.S. Pat. No. 5,124,605 intersperses a series of compliant tubes between the hub and the rim. All of these structures typically comprise multiple mechanical elements, adding considerable complexity, cost and reliability issues to the basic rotating rim flywheel design.
There have been several attempts to create safe, high performance flywheel rotors by combining the use of composite materials with classical isotropic rotor designs. For example, Rabenhorst et. al., in U.S. Pat. No. 3,788,162, show a rotor of the constant stress design comprising multiple fiber reinforced composite laminations to build up the radially contoured shape. Unfortunately, such a construction makes only limited use of the highly directional strength properties of the fibers and thus cannot offer the full performance advantage of the fiber properties. Gilman, in U.S. Pat. No. 4,186,245, shows a similar constant stress disc construction built up using high specific strength metal alloy strips. Gilman's design has high volumetric efficiency due to the efficient packing of the strips but the design fails to take into account the poor fatigue characteristics of the chosen glassy metal alloy materials. Kulkarni and Stone in U.S. Pat. No. 4,408,500 show an isotropic constant stress disc flywheel rotor with an outer rim of uniaxial fiber reinforced composite intended to improve the safety of the device. While incipient failure in the rim of Kulkari and Stone's rotor may give some warning, full rotor burst will still generate the large and destructive ballistic particles characteristic of conventional isotropic rotors.
Thus, as a result of the aforementioned limitations and despite the efforts over several decades of many workers skilled in the art, energy storage flywheels have still not been adopted for widespread use in the transportation, space and utility power industries.